1. Field of the Invention
The present invention is directed to a system for computing a continuous local neighborhood of a point on a polygonal mesh, which neighborhood may be used to compute a continuous local parameterization of the mesh.
2. Description of the Related Art
FIG. 1 shows a mapping between a 3D polygonal surface 100 and a 2D image or domain 102. The mapping or parameterization of polygonal geometric surfaces is sometimes referred to as image mapping, a category of techniques that includes texture mapping, reflection or environment mapping, bump mapping, light mapping, etc. Image mapping associates coordinates 103 in image space 102 with locations 104 on the surface 100 of a geometric object. The discrete samples of an image raster addressed by the coordinates in image space 102 are applied to the geometric object or surface 100.
Image mapping, a form of parameterizing, is a standard technique for adding visual details to 3D models. Nevertheless, image mapping tools are lacking, and defining a high quality parameterization for image mapping a 2D domain to a 3D polygonal model is a tedious process, even for experienced and skilled users.
What is needed is a system for defining a smoothly changing neighborhood of a polygon mesh surface, and using that smoothly changing neighborhood to compute a local parameterization that changes smoothly as a local area of the surface changes.